Putcha semigroups

  • Attila Nagy
Chapter
Part of the Advances in Mathematics book series (ADMA, volume 1)

Abstract

In [80], M.S. Putcha characterized semigroups which are decomposable into semilattice of archimedean semigroups. He showed that a semigroup S is a semilattice of archimeden semigroups if and only if, for every a, bS, the assumption aS 1 bS 1 implies a n S 1 a 2 S 1 for some positive integer n. Semigroups with this condition are called Putcha semigroups. In this chapter we also consider the left Putca semigroups and the right Putcha semigroups (Definition 2.1). It is proved that a semigroup is a simple left and right Putcha semigroup if and only if it is completely simple. By the help of this result, the retract extension of completely simple semigroups by nil semigroups are characterized. It is shown that a semigroup is a retract extension of a completely simple semigroup by a nil semigroup if and only if it is an archimedean left and right Putcha semigroup containing at least one idempotent element.

Keywords

Positive Integer Arbitrary Element Simple Semigroup Idempotent Element Ideal Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Attila Nagy
    • 1
  1. 1.Department of Algebra, Institute of MathematicsBudapest University of Technology and EconomicsHungary

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